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This article is devoted to the study of a perturbation with a viscosity term
in an elliptic equation involving the p-Laplacian operator and related to
the best contant problem in Sobolev inequalities in the critical case.
We prove first that this problem, together with the equation, is stable
under this perturbation, assuming some conditions on the datas. In the
next section, we show that the zero solution is strongly isolated in some
sense, among the space of the solutions. Actually, we end the...
We prove the periodicity of all H2-local minimizers with low energy
for a one-dimensional higher order variational problem.
The results extend and complement an earlier work of Stefan Müller
which concerns the structure of global minimizer.
The energy functional studied in this work is motivated by the
investigation of coherent solid phase transformations and the
competition between the
effects from regularization and formation of small scale structures.
With a special choice of a bilinear double...
In this paper sufficient second order optimality conditions for optimal control problems
subject to stationary variational inequalities of obstacle type are derived. Since
optimality conditions for such problems always involve measures as Lagrange multipliers,
which impede the use of efficient Newton type methods, a family of regularized problems is
introduced. Second order sufficient optimality conditions are derived for the regularized
problems...
In this paper sufficient second order optimality conditions for optimal control problems
subject to stationary variational inequalities of obstacle type are derived. Since
optimality conditions for such problems always involve measures as Lagrange multipliers,
which impede the use of efficient Newton type methods, a family of regularized problems is
introduced. Second order sufficient optimality conditions are derived for the regularized
problems...
We study optimal control problems for partial differential equations (focusing on the multidimensional differential equation) with control functions in the Dirichlet boundary conditions under pointwise control (and we admit state - by assuming weak hypotheses) constraints.
We consider the functional
where is a bounded domain and is a convex function. Under general assumptions on , Crasta [Cr1] has shown that if admits a minimizer in depending only on the distance from the boundary of , then must be a ball. With some restrictions on , we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these...
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